Physics-based machine learning for computational fracture mechanics

Abstract This study introduces a physics-based machine learning ( $$\phi $$ ϕ ML) framework for modeling both brittle and ductile fractures in elastic-viscoplastic materials. It integrates physical principles, including governing equations and constraints, directly into the neural network architecture. Specifically, a feedforward neural network is designed to embed physical laws within its architecture, ensuring thermodynamic consistency. Building on this foundation, synthetic datasets generated from finite element-based phase-field fracture simulations are employed to train the proposed framework, focusing on capturing the homogeneous, one-dimensional fracture responses. Detailed analyses are performed on the stored elastic energy and the dissipated work due to plasticity and fracture, demonstrating the capability of the framework to predict essential fracture features. The proposed $$\phi $$ ϕ ML framework overcomes the shortcomings of classical machine